Simplify: (2+log(x^2y^2))/log(10xy) The result should be 2. Not sure how to get it though.

We are asked to simplify `(2+logx^2y^2)/(log10xy)`

We will use the following properties of logarithms:

`(1) logAB=logA+logB`

`(2) log(A/B)=logA-logB`

`(3) logA^n=n logA`

`(2+logx^2y^2)/(log10xy) `

`=(2+logx^2+logy^2)/(log10+logx+logy) `

`=(2+2logx+2logy)/(1+logx+logy) `

`=(2(1+logx+logy))/(1+logx+logy) `

`=2 `

We used log10=1 since the base of the common logarithm is 10.